Combinatorial Constructions of Optimal Three-Dimensional Optical Orthogonal Codes

In this paper, we study three-dimensional (u × v× w, k, λ) optical orthogonal codes (OOCs) with at most one optical pulse per wavelength/time plane (AM-OPP) restriction, which is denoted by AM-OPP 3-D (u × v × w, k, λ)-OOC. We build an equivalence relation between such an OOC and a certain combinatorial subject, called a w-cyclic group divisible packing of type (vw)^u. By this link, the upper bound of the number of codewords is improved and some new combinatorial constructions are presented. As an application, the exact number of codewords of an optimal AM-OPP 3-D (u × v × w, 3, 1)-OOC is determined for any positive integers v, w, and u ≠ 2 (mod 6) with some possible exceptions.